Physics: CUET Mock Test - 8 - JEE MCQ

Given: V₂ = 10 V; V₁ = 20 V; C = 5 μF; Inductance (I) = 0.5 mH
Initial charge on the capacitor (q₁) = C × V₁ = 5 × 10^-6 × 20 ……………….1
q₁ = 10^-4 C …………..B
The instantaneous charge on the capacitor as the capacitor discharges through the inductor ⇒ q₂
q₂ = q₁cos (ωt) ⇒ q₂/q₂ = cos (ωt) ………………..A
Also, q₂ = C × V₂ = 5 × 10^-6 × 10 …………………….2
q₂ = 0.5 × 10^-4 C
From 1 and 2 ⇒ q₂/q₂ = V₂V₁ ⇒ q₂/q₂ = 0.5 = 1/2
From equation A, we can equate as follows ⇒ cos (ωt) = 12
ωt = π/2 rad ………………..3
For an LC circuit ⇒ 
ω=20000rad/s …………………….4
The current through the circuit is given as:
Current (I)=-dq/dt
Charge decreases with respect to time, so, dq/dt obtained will be negative and this is why we add a negative sign to make a current

The most common application of LC oscillators is radio transmitters and receivers. LC oscillators have good phase noise characteristics as well as offer ease of implementation. Due to these factors, LC oscillators are most commonly used in radio-frequency circuits.

When we are connecting a charged capacitor to an inductor, the electric current in the circuit and charge on the capacitor undergoes LC oscillations. All the others are incorrect statements regarding LC Oscillations.

The self-inductance of a coil is said to be one henry if an induced emf of one volt is set up in it when the current in it changes at the rate of one ampere per second. Self inductance is defined as the induction of a voltage in a current-carrying wire when the current in the wire itself is changing.

Self-inductance is directly proportional to the number of turns and the area of cross-section. The self-inductance of a solenoid increases μ_r times if it is wound over an iron core of relative permeability μ_r.

The mutual inductance of two coils is the property of their combination. It does not matter which one of them functions as the primary or the secondary coil. Hence, mutual inductance does not depend on reciprocity.

NΦ = MI
200 × 500 = M × 10
M = 10⁴ H

Self-inductance = Magnetic flux / Current
Self inductance = 10×10^-6 / 5 × 10^-3
Self inductance = 2 × 10^-3 H
Self inductance = 2mH

Self-inductance = Magnetic flux / Current
Self-inductance = 50×10⁻³/5
Self-inductance = 1 × 10^-2 Wb

Mutual Inductance is the interaction of one coils magnetic field on another coil as it induces a voltage in the adjacent coil. Unit of Mutual inductance = V / As⁻¹.
SI unit = VsA^-1.

Self-inductance = 

Magnetic flu x Current

Self-inductance = [M L² T^-2 A^-2]

Magnetization is also termed as magnetic polarization. Magnetic polarization is basically a balance between the magnetic flux density in a space which is devoid of matter and the magnetic flux density in a space with matter, i.e. in a material.

The statement magnetic intensity and intensity of magnetization are the same is the false one. They are not the same. When a magnet is entering a magnetic field, then the poles of the magnet experiences certain forces. Magnetic intensity refers to the measure of these forces. But, the intensity of magnetization explains the change in the magnetic moment of a magnet as a function of volume. All the other statements are valid.

Diamagnetic materials are those which when placed in a magnetizing field are feebly magnetized in a direction opposite to that of the magnetizing field. Therefore, it is feebly repelled by a magnet. Example: zinc, gold, etc.

The relative permeability of ferromagnetic materials is much larger than 1. Ferromagnetic substances are those, which when placed in a magnetic field are strongly magnetized in the direction of the magnetizing field, i.e., it is strongly attracted by a magnet.

Diamagnetic materials have a small and negative value of magnetic susceptibility. Paramagnetic materials have a small and positive value of magnetic susceptibility and ferromagnetic materials have a large and positive value of magnetic susceptibility.

Iron is a ferromagnetic material. Ferromagnetism decreases with a rise in temperature, and above a certain temperature called “Curie’s temperature,” ferromagnets become paramagnets. For iron, it is approximately, 800 °C.

Permanent magnets are made up of materials having high retentivity, high coercivity, and high permeability such as steel. Other suitable materials for making permanent magnets are alnico (an alloy of iron, aluminum, nickel, copper, and cobalt), cobalt steel, and ticonal. That leaves zinc as the one that cannot be used to make permanent magnets.

The magnetic susceptibility of diamagnetic materials doesn’t depend upon temperature. This is often because there’s an outsized barrier between the bottom state and therefore the excited states of diamagnetic substances. Hence, it remains constant during the change of temperature. All the other statements are false.

Curie’s law in magnetism states that the magnetic susceptibility of paramagnetic materials is inversely proportional to its absolute temperature and it is given by:
χ_m = C/T

Paramagnetic materials are those when suspended freely inside the magnetic field, it slowly sets itself parallel to the direction of the magnetic field. When placed in a non-uniform magnetic field, it tends to move from weaker to a stronger magnetic field.

When suspended freely, a thin long piece of magnet comes to rest nearly in the geographical north-south direction. When placed in a non-uniform magnetic field, it tends to move from weaker to stronger magnetic field.

The magnetic dipole moment of a magnetic dipole is defined as the product of its pole strength and magnetic length. The SI unit of magnetic dipole moment is ampere metre2 (Am2). Magnetic dipole moment is a vector quantity and is directed from south to north pole of the magnet.

Magnetic dipole moment = Pole strength × Magnetic length.
Magnetic dipole moment = 20 Am × 0.1 m
Magnetic dipole moment = 2 Am².

Magnetic dipole moment = Pole strength × Magnetic length.
Pole strength = Magnetic dipole moment / Magnetic length
Pole strength = 5 / 0.2
Pole strength = 25 Am.

Torque, τ = mBsin (θ).
Given: m = 20 J/T; B =9 T; θ = 60^o
τ = 20 JT^-1 × 9 T × sin(60^o)
τ = 155.8J.

A magnet can attract another magnet or a magnetic substance like iron. However, a magnet can repel another magnet only. So repulsion is the surer test of magnetism.

Pieces of naturally occurring iron ore, lodestone or magnetite had the property of attracting small pieces of iron. Hence, magnetite is a natural magnet. All natural magnets are permanent magnets, meaning they will never lose their magnetic power.

Attractive property, directive property and the law of magnetic poles are some of the important properties of magnets. So unlike electric charges, magnetic monopoles do not exist. Every magnet exists as a dipole.